2017/09/04 by Bell, G., Głodkowski, D., Nagórko, A. · 1 citation
#20F69 (secondary) #54F45 (primary) #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1709.01119
We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition complexity. Moreover, finite APC-decomposition complexity implies property A for metric spaces. We also show that finite APC-decomposition complexity is preserved by direct products of groups and spaces, amalgamated products of groups, and group extensions, among other constructions.